(i) First of all, we note that Eq. (REF ) is completely independent of the details of \(CP\)  violation in the RHN sector.
\(CP\)  violation in RHN decays is typically quantified by \(CP\)  asymmetry parameters \(\varepsilon _{i\alpha }\)  [1]}; these parameters, however, do not appear in our analysis and are in any case severely suppressed for RHN masses as low as a few 100 TeV (barring a resonant enhancement).
This observation is in accord with our discussion in Sec.  and reflects the fact that wash-in leptogenesis allows us to separate the scales of \(CP\)  and \(B\!-\!L\)  violation.
The RHN interactions at low temperatures only serve the purpose to violate lepton number; the violation of \(CP\)  invariance is delegated to higher temperatures and accomplished by axion inflation.
At the time of wash-in leptogenesis, the \(CP\) -violating initial conditions set by axion inflation are then encoded in the remaining conserved global charges, i.e., the global right-handed electron number in our benchmark example.
